CN1343388A - Method and device for separating mixture of source signals - Google Patents

Abstract

Device and method for separating a mixture of source signals to regain the source signals, the device and method being based on measured signals, the invention comprises: bringing each measured signal to a separation structure including an adaptive filter, the adaptive filter comprising filter coefficients; using a generalised criterion function for obtaining the filter coefficients, the generalised criterion function comprising cross correlation functions and a weighting matrix, the cross correlation functions being dependent on the filter coefficients; estimating the filter coefficients, the resulting estimates of the filter coefficients corresponding to a minimum value of the generalised criterion function; and updating the adaptive filter with the filter coefficients.

Description

The method and apparatus of separating mixture of source signals

Technical field

The present invention relates to be used for a kind of method and apparatus that separating mixture of source signals is recaptured source signal.

Background of invention

Several pieces of articles [1～3,8,17,19,20] have been delivered recently about how separating dynamic mixed signal.In principle, it is possible only utilizing second-order statistics to come the separation source signal, with reference to [8].There are several pieces of articles to solve Blind Signal Separation problem, with reference to [3,20] with dynamic/convolution mixed signal at frequency domain.The purpose of in frequency domain dynamic source signal being separated is the separation problem that solves a plurality of static state/transient state source signal, one of each frequency separation.In order to obtain dynamic channel system (hybrid matrix), must carry out interpolation corresponding to the estimation in different frequency interval.It is not too loaded down with trivial details that this process appears to, and reason is calibration and displacement uncertain [16].Method herein is a kind of " time domain approach ", sees [8], and it is simulated the unit of channel system with finite impulse response filter (FIR), thereby avoids this uncertainty.

Pham and Garat have illustrated a kind of accurate maximum likelihood method of carrying out Signal Separation by second-order statistics in [11].Provided a kind of algorithm at the statistics mixed signal, just at the hybrid matrix that does not have to postpone.Each the signal S that separates _i, i=1 ..., M uses a linear time invariant (LTI) filter h _iCarry out filtering.The criterion that adopts is the cross-correlation that estimates for the later signal of these filtering.According to [11], filter h _iOptimal selection be the filter that frequency response follows the spectrum density of respective sources signal to be inversely proportional to.So these filters h _i, i=1 ..., M is a prewhitening filter.But the spectrum density of source signal usually is ignorant, or even along with the time changes.A kind of method is to estimate these filters according to the predicated error that the mode of this paper and [1] provide.In addition, [8] algorithm of listing still has many problems not solve.

Principal character of the present invention

The present invention, just separating mixture of source signals regains the method for source signal, it is characterized in that this sef-adapting filter comprises filter coefficient with comprising that an isolating construction of sef-adapting filter separates each measured signal; Obtain these filter coefficients with a general criterion function, this general criterion function comprises cross-correlation function and a weighting matrix, and this cross-correlation function depends on filter coefficient; Estimate these filter coefficients, the estimation of the filter coefficient that obtains is corresponding to general criterion minimum of a function value; And with this sef-adapting filter of these filter coefficient updates.

The present invention, just separating mixture of source signals regains the device of source signal, further feature is, the input of this device is measured signal, this device comprises: be used for measured signal is passed to the signaling link of the isolating construction that comprises a sef-adapting filter, this sef-adapting filter comprises filter coefficient; Be used to obtain a general criterion functional unit of these filter coefficients, this general criterion functional unit comprises cross-correlation function and a weighting matrix, and this cross-correlation function depends on these filter coefficients; Estimate the device of these filter coefficients, the estimation of the filter coefficient that obtains is exported corresponding to general criterion minimum of a function value; And with the updating device of these these sef-adapting filters of filter coefficient update.

Concrete application of the present invention comprises the medical measuring device that mobile phone technology, data communication, hearing aids and ECG are such.Also comprise the echo cancellation technology of usually running in the communications field.

The accompanying drawing summary

Fig. 1 explanation is with the empirical parameter variance and the actual parameter variance of preferred embodiment among the present invention relatively of prior art signal separation algorithm.

Fig. 2 explanation with in the preferred embodiment among the present invention relatively of prior art signal separation algorithm as the estimated mean value of the function of relative frequency.

Fig. 3 explanation with in the preferred embodiment among the present invention relatively of prior art signal separation algorithm as the function parameters variance of relative frequency.

Preferred embodiment

The present invention derives and has provided a signal separation algorithm.The main result of this analysis is a preferred weighting matrix.This weighting matrix is used to realize separating the algorithm of dynamic mixed signal.This algorithm that obtains can improve the parameter Estimation performance significantly under source signal has the situation of similar frequency spectrum.In addition, in the time of given a plurality of known parameters, this parameters analysis method can be used in and extracts obtainable (asymptotic) parameter variance.

Source signal herein is a M mutual incoherent white sequences.These white sequences are called the signal that the source produces, and use ξ _k(n) expression, k=1 wherein ..., M.The signal that these sources are produced carries out convolution G with the linear time-varying filtering device _k(q)/F _k(q), the result is: x (n)=[x ₁(n) ... x _M(n)] ^T=K (q) ξ (n) $=\mathrm{diag}(\frac{G_1\left(q\right)}{F_1\left(q\right)},\·\·\·,\frac{G_M\left(q\right)}{F_M\left(q\right)})\left[\begin{array}{c}{\mathrm{\ξ}}_1\left(n\right)\\ \·\\ \·\\ \·\\ {\mathrm{\ξ}}_M\left(n\right)\end{array}\right],$ Be called source signal, wherein q and T are respectively time migration operator and matrix transpose.Introduce following hypothesis.

A1. the signal of Chan Shenging is that a mean value is 0 the white Gaussian process of stable state:

ζ(n)∈N(0，∑)， ∑＝diag(σ ₁ ²，…，σ _M ²)

The element of A2.K (q) is the asymptotic filter of stablizing and having minimum phase.

Owing to made Gauss's hypothesis, so condition A1 is the comparison harshness.But,, seem very difficulty otherwise assess some statistical expectations unless adopt Gauss's hypothesis.

Source signal x (n) is immeasurable, and they are transfused to a system that is called channel system.

Y (n)=[y ₁(n) ..., y _M(n)] ^T=B (q) x (n) can measure, and is called measured value.Channel system B (q) is in this article:

B wherein _Ij(q), i, j=1 ..., M is a finite impulse response filter.Purpose is an extraction source signal from these measured values.This extraction can be to utilize the self adaptation isolating construction, with reference to [8].What input to this isolating construction is the signal that can observe.The output S of isolating construction ₁(n) ..., S _M(n) depend on sef-adapting filter, D _Ij(q, θ), i, j=1 ..., M can be write as

S (n, θ)=[S ₁(n, θ) ..., S _M(n, θ)] ^T(wherein θ is a parameter vector that comprises the filter coefficient of sef-adapting filter to=D for q, θ) y (n).That is to say that this parameter vector is Q=[d ₁₁ ^T..., d _MM ^T] ^T, d wherein _Ij, i, j=1 ..., M comprises D respectively _Ij(q, θ), i, j=1 ..., the vector of the coefficient of M.Notice that different with B (q), (q θ) does not comprise a fixing diagonal to separation matrix D, with reference to [6,13].

Most expression formulas herein and calculating all are the situations at two two outputs of input (TITO), M=2.Utilizing the main cause of the situation of two outputs of two inputs is that they are that parameter is confirmable under a set condition, with reference to [8].But the analysis of this paper also can be applied to more generally multiple-input and multiple-output (MIMO) situation, as long as they also are that parameter is confirmable.

Following formula can obtain y ₁(n) and y ₂(n) a N sample, the criterion function that [8] propose is $\stackrel{-}{V}\left(\mathrm{\&theta;}\right)=\underset{k=-U}{\overset{U}{\mathrm{\&Sigma;}}}{\stackrel{\&CenterDot;}{R}}_{y_1{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="A0080477300181.png,A0080477300191.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}^2(k;\mathrm{\&theta;}),$ Wherein ${\stackrel{\&CenterDot;}{R}}_{y_1{y}_2}(k;\mathrm{\&theta;})=\frac{1}{N}\underset{n=0}{\overset{N-k-l}{\mathrm{\&Sigma;}}}{s}_1(n;\mathrm{\&theta;})s_2(n+k;\mathrm{\&theta;}),k=0,\&CenterDot;\&CenterDot;\&CenterDot;,U.$ In order to emphasize dependence, equation (2.6) can be write as θ ${\stackrel{\&CenterDot;}{R}}_{y_1{y}_2}(k;\mathrm{\&theta;})={\stackrel{\&CenterDot;}{R}}_{y_1{y}_2}\left(k\right)-\underset{i}{\mathrm{\&Sigma;}}{d}_{12}\left(i\right){\stackrel{\&CenterDot;}{R}}_{y_2{y}_2}(k-i)$ $-\underset{i}{\mathrm{\&Sigma;}}{d}_{21}\left(i\right){\stackrel{\&CenterDot;}{R}}_{y_1{y}_2}(k+i)+\underset{i}{\mathrm{\&Sigma;}}\underset{l}{\mathrm{\&Sigma;}}{d}_{12}\left(i\right)d_{21}\left(l\right){\stackrel{\&CenterDot;}{R}}_{y_2{y}_1}(k-i+l),$ D wherein ₁₂(i) expression filter D ₁₂(q) i coefficient.

For simplicity, introduce following vector ${\stackrel{\&CenterDot;}{r}}_N\left(\mathrm{\&theta;}\right)={[{\stackrel{\&CenterDot;}{R}}_{y_1{y}_2}(-U,\mathrm{\&theta;})\&CenterDot;\&CenterDot;\&CenterDot;{\stackrel{\&CenterDot;}{R}}_{y_1{y}_2}(U,\mathrm{\&theta;})]}^T$ Wherein subscript N represents that the covariance that estimates obtains from N sample.In addition, introduce a positive definite weighting matrix W (θ), it may also depend on θ.Like this, the criterion in the equation (2.6) can be write as prevailingly: $V_N\left(\mathrm{\&theta;}\right)=\frac{1}{2}{\stackrel{\&CenterDot;}{r}}_N^T\left(\mathrm{\&theta;}\right)W\left(\mathrm{\&theta;}\right){\stackrel{\&CenterDot;}{r}}_N\left(\mathrm{\&theta;}\right),$ Hereinafter will analyze this.Notice that the estimator that is studied is closely related with the nonlinear regression of research in [15].The estimation of parameters of interest is to obtain like this ${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N=\arg \underset{\mathrm{\&theta;}}{\min }{V}_N\left(\mathrm{\&theta;}\right)$

Though verified Signal Separation of carrying out on the basis of criterion (2.6) is functional, sees example [12], has two problems still unresolved in article [8].

1. find θ _NThe asymptotic distribution of estimation make the people interested.Particularly the expression formula of asymptotic covariance matrix makes us very interested.One of reason is that the user can assess the performance of various mixed structures, and need not carry out emulation.Can also further understand the mixed signal that is difficult to separate which kind of type.This asymptotic covariance matrix also makes the user this performance can be compared with Cramer-Rao lower boundary (CRB), mainly is to analyze this method how far the optimum performance of prediction error methods is differed.Can in [14], find CRB to analyze to the MIMO situation.

2. how to be the highest (asymptotic) accuracy selection weighting matrix W (θ)? provide best weighting and asymptotic distribution, just can further analyze the weighting of when only using W (θ) ≠ I, wherein I is a unit matrix.

The purpose of this piece article is:

● find out θ _NThe asymptotic distribution of estimation.

● find the weighting matrix W (θ) that makes asymptotic precision the highest.

● how research realizes optimum weighting scheme.

Except A1 and A2, establish in the following description:

A3. the condition C 3～C6 in the hypothesis [8] satisfies, so the dual input double-outputting system that is studied is that parameter is confirmable.

(minimum) value of A4.U is according to 5 definition of the proposition in [8].

A5. ‖ θ ‖＜∞ that is to say, θ ₀Be to compact D _MAn interior point.Here, θ ₀Comprise real parameter.

This part begins to carry out statistical analysis from consistency.Come to determine Q in such a way _N(Q^ _N) the asymptotic property (in the time of N → ∞) of estimation.But, at first carry out some and observe in advance.In [8], illustrated

1. in the time of N → ∞, Probability be 1 (w.p.1).Like this

V _N(θ) → and V (θ), w.p.l, wherein $\stackrel{\&OverBar;}{V}\left(\mathrm{\&theta;}\right)=\frac{1}{2}{r}^T\left(\mathrm{\&theta;}\right)W\left(\mathrm{\&theta;}\right)r\left(\mathrm{\&theta;}\right),r\left(\mathrm{\&theta;}\right)={[R_{y_1{y}_2}(-U,\mathrm{\&theta;})\&CenterDot;\&CenterDot;\&CenterDot;R_{y_1{y}_2}(U,\mathrm{\&theta;})]}^T.$ Wherein at set D _MIn the convergence of (3.1) be consistent, here θ is a member $\underset{N\&RightArrow;\&infin;}{\lim }\underset{\mathrm{\&theta;}\&Element;D_M}{\sup }\left|\right|V_N\left(\mathrm{\&theta;}\right)-\stackrel{\&OverBar;}{V}\left(\mathrm{\&theta;}\right)\left|\right|=0,---w.p.l.$

In addition because the isolating construction that adopts is the finite impulse response type, so for N than some N ₀＜∞ is big, and gradient is a bounded $\underset{l\&le;i\&le;\mathrm{n\&theta;}}{\max }\left\{\underset{\mathrm{\&theta;}\&Element;D_M}{\sup }\right|\frac{\&PartialD;V_N\left(\mathrm{\&theta;}\right)}{\&PartialD;{\mathrm{\&theta;}}_i}\left|\right\}\&le;C---w.p.l,$

In equation (3.4), C is a constant, C＜∞, and n θ represents the dimension of θ.More than discussion and confirmability analysis [8] obtain to draw a conclusion:

Conclusion 1: in the time of N → ∞, ${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N\&RightArrow;{\mathrm{\&theta;}}_0---w.p.l.$

Set up after (by force) consistency, consider θ ^ _NAsymptotic distribution.Because θ ^ _NMake criterion V _N(θ) minimum, V ' _N(θ ^ _N)=0, wherein V ' _NExpression V _NGradient.According to average value theorem, $O=V_N^{\&prime;}\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N\right)=V_N^{\&prime;}\left({\mathrm{\&theta;}}_0\right)+V_N^{\&prime;\&prime;}\left({\mathrm{\&theta;}}_{\&Element;}\right)({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N-{\mathrm{\&theta;}}_0),$ θ wherein _ξAt θ ^ _NWith θ ₀Between straight line on.Note, because θ ^ _NBe consistent, so in the time of N → ∞, θ ^ _N-θ ₀Thereby θ _ξ-θ ₀Also be consistent.

Next step analyzes θ ₀Gradient (to describe simply in order making, to suppose W (θ)=W)

Wherein $\stackrel{\&CenterDot;}{G}=\frac{\&PartialD;{\stackrel{\&CenterDot;}{r}}_N\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}{|}_{\mathrm{\&theta;}={\mathrm{\&theta;}}_0},$

Notice that the calculating of G is directly carried out, for example with reference to [8].Being similar to of introducing can not influence gradation, is tending towards 0 speed ratio r because this has been an error _N(θ ₀) (r^ _N(θ ₀)) estimation want fast.In addition, because r _N(θ)=0, V _N' (θ) asymptotic distribution is with G ^TWr^ _N(θ ₀) asymptotic distribution identical, wherein $G=\frac{\&PartialD;r\left(\mathrm{\&theta;}\right)}{\&PartialD;\mathrm{\&theta;}}{|}_{\mathrm{\&theta;}={\mathrm{\&theta;}}_0}$

Utilize in [15] lemma B.3, and utilize S ₁(n; θ ₀) and S ₂(n; θ ₀) all be this fact of steady-state process, can find

Convergence in distribution to a Gaussian random vector, just $\sqrt{N}{G}^{T}W{\stackrel{\&CenterDot;}{r}}_N\left({\mathrm{\&theta;}}_0\right)\&Element;\mathrm{AsN}(0,G^T\mathrm{WMWG}),$ Wherein $M=\underset{N\&RightArrow;\&infin;}{\lim }\mathrm{NE}\left[{\stackrel{\&CenterDot;}{r}}_N\left({\mathrm{\&theta;}}_0\right){\stackrel{\&CenterDot;}{r}}_N^T\left({\mathrm{\&theta;}}_0\right)\right].$ This means that gradient vector is that asymptotic normality distributes, have 0 mean value, covariance matrix is M.

Before providing the Main Conclusions of this paper, must study the Hessian matrix V earlier " _NThe convergence situation.Suppose to exist the limit, definition ${\stackrel{\&OverBar;}{V}}^{\&prime;\&prime;}\left(\mathrm{\&theta;}\right)=\underset{N\&RightArrow;\&infin;}{\lim }{V}_N^{\&prime;\&prime;}\left(\mathrm{\&theta;}\right).$ In order to make V " _N(θ _ξ) convergence, use following (standard) inequality

‖ V _N" (θ _ξ)-V " (θ ₀) ‖ _F≤ ‖ V _N" (θ _ξ)-V _N" (θ ₀) ‖ _F+ ‖ V _N" (θ ₀)-V " (θ ₀) ‖ _F, ‖ ‖ wherein _FExpression Frobenius mould.Because the finite impulse response isolating construction, second dervative is continuous.In addition, because θ _ξConvergence with probability 1 is to θ ₀So, first convergence with probability 1 to 0.Second also convergence with probability 1 to 0.This can be with illustrating with explanation (3.3) similar methods.Be also noted that because three order derivatives are bounded, so convergence is consistent about θ.

Can directly find out Hessian V now ^-' ' can be write as ${\stackrel{\&OverBar;}{V}}^{\&prime;\&prime;}\left({\mathrm{\&theta;}}_0\right)=\underset{N\&RightArrow;\&infin;}{\lim }{V}^{\&prime;\&prime;}\left({\mathrm{\&theta;}}_0\right)=G^T\mathrm{WG}---w.p.l.$ Like this for very big N, $\sqrt{N}({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N-{\mathrm{\&theta;}}_0)\&ap;\sqrt{N}{\left(G^T\mathrm{WG}\right)}^{-1}{G}^{T}W{\stackrel{\&CenterDot;}{r}}_N\left({\mathrm{\&theta;}}_0\right),$ Suppose to exist contrary (guaranteeing) by the confirmability condition among the A3.Here, be tending towards 0 speed all than

Want fast all approximate errors all to be left in the basket.At last, can obtain to draw a conclusion.

Consideration is based on the signal separating method of second-order statistics, wherein θ ^ _NObtain from (2.10).So standard error of estimate

A 0 limited average Gaussian Profile is arranged. $\sqrt{N}({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N-{\mathrm{\&theta;}}_0)\&Element;\mathrm{AsN}(0,P),$ Wherein

P=(G ^TWG) ^-1G ^TWMWG (G ^TWG) ^-1Obviously, matrix M is a dominant role, and it is significant finding out a clearer and more definite expression formula.For simplicity, we only consider that the signal that produces is the situation (illustrated as hypothesis) of 0 average white Gaussian signal.Seem that it is very difficult will finding the explicit expression of non-Gauss's situation.Be also noted that the normality assumption among the A1 is vital.For example, under more weak hypothesis

Asymptotic normality set up.

[5] the theorem 6.4.1 in accurately illustrates the component that how to calculate M.In fact calculate these elements and be very easy to, below this point will be described.Order ${\mathrm{\&beta;}}_r=\underset{p=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{R}_{y_1{y}_1}(p;{\mathrm{\&theta;}}_0)R_{y_2{y}_2}(p+r;{\mathrm{\&theta;}}_0).$ In addition, introduce following Z-transformation, ${\mathrm{\&Phi;}}_1\left(z\right)=\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{R}_{y_1{y}_1}(k;{\mathrm{\&theta;}}_0)z^{-k},$ ${\mathrm{\&Phi;}}_2\left(z\right)=\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{R}_{y_2{y}_2}(k;{\mathrm{\&theta;}}_0)z^{-k}.$ So $\underset{r=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{p=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{R}_{y_1{y}_1}(p;{\mathrm{\&theta;}}_0)R_{y_2{y}_2}(p+r;{\mathrm{\&theta;}}_0)z^{-r}={\mathrm{\&Phi;}}_1\left(z^{-1}\right){\mathrm{\&Phi;}}_2\left(z\right).$ Like this, β _τBe the covariance of ARMA process, power spectrum is ${\mathrm{\&Phi;}}_1\left(z^{-1}\right){\mathrm{\&Phi;}}_2\left(z\right)={\mathrm{\&sigma;}}_1^3{\mathrm{\&sigma;}}_2^2(1-B_{12}\left(z\right)B_{21}\left(z\right){)}^3(1-{\stackrel{\&OverBar;}{B}}_{12}\left(z^{-1}\right){\stackrel{\&OverBar;}{B}}_{31}\left(z^{-1}\right)){\left|\frac{G_1\left(z\right)}{F_1\left(z\right)}\right|}^2<msup>\; <none>\; </none>\; </msup>{\left|\frac{G_2\left(z\right)}{F_2\left(z\right)}\right|}^2.$

The calculating of ARMA covariance has the simple but effective method of standard, for example sees [15, appendix C 7.7].For τ=0 ..., 2U, given β _τ, weighting matrix can be expressed as

Like this, in this problem, the signal of separation is by the determinant distortion of channel system, the determinant of this channel system equal det (B (z) }, reconstruction signal can be expressed as ${\stackrel{\&CenterDot;}{r}}_i\left(n\right)=\frac{1}{\det \left\{D(q,\stackrel{\&CenterDot;}{\mathrm{\&theta;}})\right\}}{s}_i(n;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_N),$ As long as det{D (q, θ ₀) have a minimum phase.

In order to finish our discussion, how also to point out compute matrix G.The element of G all calculates in the following manner.Utilize equation (2.8), obtain $\frac{\&PartialD;R_{y_1{y}_2}(k;\mathrm{\&theta;})}{\&PartialD;d_{21}\left(i\right)}=-R_{y_1{y}_1}(k+i)+\underset{l}{\mathrm{\&Sigma;}}{d}_{12}\left(l\right)R_{y_2{y}_1}(k-l+i)$ $\frac{\&PartialD;R_{y_1{y}_2}(k;\mathrm{\&theta;})}{\&PartialD;d_{12}\left(i\right)}=-R_{y_2{y}_2}(k-i)+\underset{l}{\mathrm{\&Sigma;}}{d}_{21}\left(l\right)R_{y_2{y}_1}(k+i-l).$ They can directly be calculated.

Next step considers how to select W.Our discovery is as follows.The θ ^ that obtains as the minimum variable of criterion (2.10) _NAsymptotic precision optimum under following situation

W=W ₀=M ^-1Power is chosen as for this reason:

P(W ₀)＝(G ^TM ^-1G) ^-1

For all positive definite weighting matrix W, P (W ₀)-P (W) is positive semi-definite, and in this sense, this precision is the highest.

Its proof comes from famous matrix optimizing result, for example with reference to [9, appendix 2].

Can directly obtain this result from the ABC theorem in [15, appendix C 4.4].But top itself is a useful results as a result, and it has promoted the analysis of this paper.

Before the practical application of considering this preferred weighting scheme, how the let us explanation selects U.This parameter is user-defined, is interesting to how selecting it to analyze.Note, suppose that A3 is the lower limit that U has provided confirmability.Following result is useful.

Following formula is weighed W with optimum ₀Being applied to criterion (2.10) gets on.Make P _U(W) expression asymptotic covariance in this case.So

P _U(W ₀) 〉=P _U-1(W ₀) just can obtain proof immediately by the calculating in [15, appendix C 4.4].Note, use optimum weighting W ₀The time, matrix { P _U(W ₀) constitute and not increase sequence.But, know the too conference destructive characteristics of value of U.This phenomenon can be understood like this, and the value of U means too greatly and need make asymptotic result effective by very big N.

The Signal Separation of relatively on Signal Separation of carrying out on the basis of algorithm of the present invention and basis, carrying out below at the algorithm of [8].This purpose relatively is explanation contribution of the present invention.In other words, understanding weighting can or can not cause parameter variance obviously to descend.In our all emulation, U=6.In addition, in several figure, used this term of relative frequency.Here relative frequency refers to f _Rel=2F/F _s, F wherein _sBe sample rate, f for example _RelEqual π!

Here channel system is by B ₁₂(q)=0.3+0.1q ^-1And B ₂₁(q)=0.1+0.7q ^-1Provide.Source signal is that the limit radius is 0.8, and angle is an AR (2) process of π/4.Second source signal also is an AR (2) process.But, the angle of adjustment limit in interval [0, pi/2], its radius 0.8 then remains unchanged.Produce 200 signals in each angle, and handled by this channel separation system and isolating construction.That is to say that for each angle, the parameter Estimation that obtains is all by on average.At last, each signal all comprises 4000 samples.

In Fig. 1, drawn empiric variance and actual parameter variance.At first to note meeting very goodly between empiric variance and the theoretical variance.Its less important attention has reduced variance significantly for the weighting that most of angles propose.In Fig. 1, parameter variance is as the function of relative frequency, and " * " represents the empiric variance in the signal separation algorithm in the prior art, the empiric variance of the method for weighting that "+" expression proposes.Solid line is the true asymptotic variance of method of weighting not, and dotted line is the true asymptotic variance with the optimum way weighting algorithm.Chain-dotted line is CRB.

Obviously, when the spectrum of source signal is closely similar, estimate very difficulty of channel parameter.In addition, in Fig. 2 and Fig. 3, provided parameter curve further.The angle of limit is in interval [40 °, 50 °].In Fig. 2, as the estimated mean value of the function of relative frequency, " * " is the emprical average of signal separation algorithm in the prior art, and "+" is the emprical average in the weighting algorithm that proposes.Solid line is corresponding to the actual parameter value.Note deviation having taken place, though littler than signal separation algorithm deviation of the prior art with the algorithm of optimum way weighting.This deviation may be because there is not the channel estimating of algorithm of weighting quite inaccurate, makes that weighting matrix is also very inaccurate to cause.In Fig. 3, with the function of parameter variance as relative frequency, " * " is the empiric variance of [8] signal separation algorithm in the prior art; "+" is the empiric variance of the weighting algorithm of proposition.Dotted line is the true asymptotic variance that does not have the algorithm of weighting, and dotted line is the true asymptotic variance with the algorithm of optimum way weighting.Chain-dotted line is CRB.Shown in Fig. 1～3, the present invention has improved the quality of Signal Separation.

According to signal separator, the further details of the present invention is repeatedly to use method of the present invention at the part of measured signal or measured signal.Also have, can also repeatedly use method of the present invention according to predetermined renewal frequency.Should be understood that predetermined renewal frequency is not necessarily invariable.Also have, the number of filter coefficient is predetermined.At last, the number of filter coefficient is predetermined in the superincumbent embodiment.

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[19] unified criterion of H.Wu and J.Principe. Blind Signal Separation and decorrelation: the emulation diagnosis of correlation matrix, Proc.of NNSP97,496-505, Amelia Island.FL, 1997.

[20] the frequency domain emulation diagnosis that separates with the J.Principe. source signal of H.Wu.JCA, 245-250, Aussois, France, 1999.

Press the modification of PCT18 system

1. separate and mix the method that source signal regains source signal, this method is based on measured signal, and this method comprises:

-each measured signal is passed to an isolating construction that comprises a sef-adapting filter, this sef-adapting filter comprises filter coefficient;

-obtaining these filter coefficients with a general criterion function, these general criterion functions comprise a cross-correlation function and a weighting matrix (W), these cross-correlation functions depend on filter coefficient;

-described weighting matrix (W) is the inverse matrix of the matrix (M) that comprises that the av covariance matrix of signal (z (t)) is estimated,

The frequency spectrum of-described signal (z (t)) is the product of the determinant estimated with the compound filter transfer function of the spectrum estimation of the source signal of coming in,

-estimation filter coefficient, the estimation of the filter coefficient that obtains is corresponding to general criterion minimum of a function value; With

-with these filter coefficient update sef-adapting filters.

2. the method for claim 1 is characterized in that the frequency spectrum of the source signal of coming in is unknown, and weighting matrix (W) has been considered the frequency spectrum of a hypothesis.

3. claim 1 or 2 method is characterized in that weighting matrix depends on filter coefficient.

4. the method for claim 1 is characterized in that, the part of measured signal or measured signal is repeatedly used this method.

5. the method for claim 4 is characterized in that, repeatedly uses this method according to predetermined renewal frequency.

6. the method for claim 1 is characterized in that, the number of filter coefficient is predetermined.

7. separate mixing the device that source signal regains source signal, is on the basis of measured signal to the input of this device, and this device comprises:

-each measured signal is passed to the signaling transmission link of an isolating construction that comprises a sef-adapting filter, this sef-adapting filter comprises filter coefficient;

-one general criterion functional unit is used to obtain filter coefficient, and this general criterion functional unit comprises a cross-correlation function and a weighting matrix (W), and these cross-correlation functions depend on filter coefficient;

-described weighting matrix (W) is the inverse matrix of the matrix (M) that comprises that the av covariance matrix of signal (z (t)) is estimated,

The frequency spectrum of-described signal (z (t)) is the product of the determinant estimated with the compound filter transfer function of the spectrum estimation of the source signal of coming in,

The device of-estimation filter coefficient, the estimation of the filter coefficient that obtains is exported corresponding to general criterion minimum of a function value; And

-become the updating device of filters with these filter coefficient update self adaptations.

8. the device of claim 7 is characterized in that, weighting matrix depends on filter coefficient.

9. the device of claim 7 is characterized in that, this device is used for separating repeatedly the part of measured signal or measured signal.

10. the device of claim 9 is characterized in that, this device is used to the part according to a predetermined renewal frequency separation measured signal or measured signal.

11. the device of claim 7 is characterized in that, the number of filter coefficient is predetermined.

Claims (10)

1. separate and mix the method that source signal regains source signal, this method is based on measured signal, and this method comprises:

-each measured signal is passed to an isolating construction that comprises a sef-adapting filter, this sef-adapting filter comprises filter coefficient;

-obtaining these filter coefficients with a general criterion function, these general criterion functions comprise cross-correlation function and a weighting matrix, these cross-correlation functions depend on filter coefficient;

-estimation filter coefficient, the estimation of the filter coefficient that obtains is corresponding to general criterion minimum of a function value; With

-with these filter coefficient update sef-adapting filters.

2. the method for claim 1 is characterized in that, weighting matrix depends on filter coefficient.

3. the method for claim 1 is characterized in that, the part of measured signal or measured signal is repeatedly used this method.

4. the method for claim 3 is characterized in that, repeatedly uses this method according to predetermined renewal frequency.

5. the method for claim 1 is characterized in that, the number of filter coefficient is predetermined.

6. separate mixing the device that source signal regains source signal, is on the basis of measured signal to the input of this device, and this device comprises:

-each measured signal is passed to the signaling link of an isolating construction that comprises a sef-adapting filter, this sef-adapting filter comprises filter coefficient;

-one general criterion functional unit is used to obtain filter coefficient, and this general criterion functional unit comprises cross-correlation function and a weighting matrix, and these cross-correlation functions depend on filter coefficient;

The device of-estimation filter coefficient, the estimation of the filter coefficient that obtains is exported corresponding to general criterion minimum of a function value; And

-become the updating device of filters with these filter coefficient update self adaptations.

7. the device of claim 6 is characterized in that, weighting matrix depends on filter coefficient.

8. the device of claim 6 is characterized in that, this device is used for separating repeatedly the part of measured signal or measured signal.

9. the device of claim 8 is characterized in that, this device is used to the part according to a predetermined renewal frequency separation measured signal or measured signal.

10. the device of claim 6 is characterized in that, the number of filter coefficient is predetermined.

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